Question

A group of college students are volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Kaitlin can paint a certain room in 3 hours. Brianna can paint the same room in 7 hours. Write an equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room? If necessary, round your answer to the nearest hundredth.

Answer 1

Answer:

The equation to find how long it will take them working together to paint the room is $\frac13+\frac17=\frac1x$.

It would require 2.1 hours to paint the room together.

Step-by-step explanation:

Given:

Number of hours required to paint the room alone by Kaitlin = 3 hours

Number of hours  to paint the room alone by Brianna = 7 hours.

We need to write the equation that can be used to find how long it will take them working together to paint the room.

Solution:

Let the time requires to paint the room when working together be denoted by 'x'.

Now we can say that:

Rate of Kaitlin to complete the job = $\frac13$

Rate of Brianna to complete the job = $\frac17$

Rate of both to complete the job = $\frac1x$

Now we can say that;'

Rate of both to complete the job  is equal to sum of Rate of Kaitlin to complete the job and Rate of Brianna to complete the job.

framing in equation form we get;

$\frac13+\frac17=\frac1x$

Hence The equation to find how long it will take them working together to paint the room is $\frac13+\frac17=\frac1x$.

Now we will take the LCM to make the denominator same we get;

$\frac{1\times 7}{3\times7}+\frac{1\times3}{7\times3}=\frac{1}x\\\\\frac{3}{21}+\frac{7}{21}=\frac1x$

Now denominator is common so we will solve for numerator we get;

$\frac{3+7}{21}=\frac1x\\\\\frac{10}{21}=\frac1x$

Now by cross multiplication we get;

$10x=21$

Dividing both side by 10 we get;

$\frac{10x}{10}=\frac{21}{10}\\\\x=2.1\ hours$

Hence It would require 2.1 hours to paint the room together.